Swept wings in transonic flow

We have already had something to say about the swept wing in Chapters 2 and 8. In this section we will look at the advantages to be gained from using swept wings in the transonic speed range, emphasising how conflicting design requirements are resolved and a suitable compromise solution is reached for a particular aircraft.

We saw in Chapter 2 that sweeping the wing works because only the velocity component at right angles to the leading edge of the wing contributes to the aerodynamic performance, and so the free stream Mach number is effect­ively reduced (Fig. 2.17). For the supersonic wing this had two advantages. Firstly the strength of the bow shock wave was reduced, and secondly the char­acteristics of the wing could be made to be similar at both low and high speeds.

In transonic flow sweep works because of the same basic principle. In the case of a typical aircraft designed only for transonic cruise, however, the oncoming flow will be just below the speed of sound and sweep is used to maintain a high cruise Mach number while reducing the effective Mach num­ber seen by the wing section to a value just below the transonic drag rise.

Sweep is therefore an important weapon in the armoury of the transonic aerodynamicist, but it has its limitations. There is still a need to use relatively thin sections in order to delay the transonic drag rise as much as possible, and consequently wings tend to be quite flexible with resulting problems which are described later. Furthermore sweep introduces problems of stability (Chap­ters 11 and 12). The lift-to-drag ratio is also reduced for the reasons given in Chapter 2.

Because of such problems sweep angle is kept as low as possible and the transonic wing section is generally still a lot thinner than its subsonic counter­part. Thus the basic low speed performance of such wings is not very good and, as would be expected with a thin section, stall occurs at a comparatively low angle of attack; an effect which is made worse by the tendency for the local load at the tip of the wing to be high, as described in Chapter 2.

It is for these reasons that such aircraft, when flying at low speed, usually require to vary the section geometry by the use of leading and trailing-edge slats and flaps. Although these are expensive in terms of weight and mechanical complexity, they do permit a thin section configuration to be adapted to give reasonable performance at low speeds. The design of such devices is a complete story in itself, since there are different performance requirements at cruise, landing, take-off and during any low speed waiting (or stand off) which may be required by air traffic control.

It must be reiterated that the use of sweep simply allows us to use a higher cruise Mach number than the drag rise Mach number for the particular wing section employed. This is merely one technique which can be employed to give acceptable cruise performance and its use is coupled with ever improving detailed section design.

In our discussion above we considered the swept wing simply from the point of view of a wing of infinite span yawed to the main flow direction. In reality, as with the supersonic swept wing, there will be both a tip section and a centre section to complicate the issue.

Furthermore, the basic planform will modify the way in which the trailing vortex sheet forms (Chapter 2). The load distribution is consequently affected so that the load becomes concentrated near the tip, as we mentioned earlier. This is just what we would wish to avoid. Firstly the concentration towards the tip means that the bending moment at the root of the wing will be more severe, and secondly the increased loading peak in the tip region will make the stalling problems there even more severe.

To compound the problem, although we may have solved some of the exist­ing problems by the use of sweep, the flexural behaviour of a conventional wing structure causes the tip angle of attack to be reduced relative to the rest

of the wing (Fig. 9.13). In some ways this is a good thing since load alleviation at the tip is what is required. However this has the effect of moving the centre of pressure of the whole wing forward and consequently altering the longitud­inal trim of the aircraft.

Looking at the above catalogue of woe, the reader might be forgiven for thinking that sweep should be avoided at all costs. This is not so. It is a vital technique in the design of aircraft of this type. However the problems discussed above will, at least, indicate that it needs to be used with due caution and that it is not such a complete answer to the proverbial maiden’s prayer as it might seem at first sight.